At present, the most generally used basic tooth profile for a gear is an involute tooth profile, and is used in various mechanical devices of the industrial society. The main advantages include the following four points. They are (a) transmission rotation is performed at a constant velocity ratio, (b) generative processing with a hob cutter is easily carried out, (c) even if a slight error occurs in the precision with which a tooth profile is processed or the precision with which a gear system is assembled, this error does not, practically speaking, adversely affect the transmission of rotation, and (d) the basic tooth profile is controlled by a module. In contrast, unsolved problems include the following six points. They are (1) during use, the slippage ratio at a tooth flank is large, thereby causing the tooth flank to wear often, (2) since protrusion flanks engage each other, contact surface pressure of the flanks of teeth is large, thereby causing wearing and pitting to occur often, (3) since stress at a dedendum based on the dedendum profile is large, the dedendum tends to break due to a high load and shock, (4) undercutting occurs in the dedendum when the number of teeth is less than or equal to a certain number of teeth during hob cutting process, (5) actually, unless there is proper backlash, it is difficult to perform smooth working rotation, and (6) a noise level that is generated during operation by, for example, vibration of a tooth or backlash is high.
To overcome these problems, many proposals have been made up until now. The historical trend of these proposals is as follows. On the one hand, involute tooth profiles are modified. On the other hand, research in new tooth profiles, typically a cycloidal tooth profile or an arcuate tooth profile, is conducted. Accordingly, further improvements are being made in various aspects.
A method of modifying a symmetrically arcuate tooth profile gear is proposed as one investigation of a new tooth profile in Japanese Examined Patent Application Publication No. 55-38541. This method is designed to prevent working of involute curves near a connection point (existing on a pitch line) of arcs. However, generative processing for purposely modifying the gear needs to be performed generation cutting again. In addition, the range and amount to be eliminated by the modification processing are not clear. Moreover, since an error in the distance between centers of a pair of gears caused by an assembly error cannot be prevented from occurring, this modification processing has almost no effect.
In addition, Japanese Examined Patent Application Publication No. 55-14934 proposes an improvement in a WN gear (Wildhaver-Novikov gear). According to the proposal of the improvement, only one point contact working, which is the greatest disadvantage of the WN gear, is modified to a two-line working. An average radius of radii of two protruding and recessed arcuate teeth profiles, at which the strengths of flanks of the teeth become greatest in the WN gear, is determined from a relational expression of an addendum length and a minimum pressure angle. In addition, a relational expression between a pressure angle and a helix angle, at which the working becomes two-lines working, is proposed. However, the WN gear cannot transmit rotation unless it is a helical gear. Necessarily, there is a limit to a tooth face, and, at the same time, a high gear cutting precision and assembly precision are required. In addition, vibration and noise are high, as a result of which the WN gear is rarely put into practical use at intermediate and high-speed regions.
In recent years, Japanese Patent No. 1606158, Japanese Examined Patent Application Publication No. 2-15743, and Japanese Unexamined Patent Application Publication No. 11-94052 have proposed a curvature wave variable gear, called a Logix gear (trade name), and improvements thereof. The main points of these proposals are that arcuate teeth profiles are provided near an working start portion of teeth flanks and an working end portion of the teeth flanks, and that a portion therebetween is connected by a continuous curve which can be differentiated and whose curvature increases and decreases periodically in a tooth depth direction. However, they do not disclose a specific differential formula and a periodical increase/decrease rate of curvature change, which are required for forming a realistic basic tooth profile curve. In particular, a method of connecting the arcs and the curve, which is most important in a tooth profile, is not made clear.
An object of the present invention is to basically overcome the aforementioned problems (1) to (4), which are not yet practically overcome by the various attempts made, by improving a tooth profile. Another object of the present invention is to provide a novel tooth profile that provides characteristics that are equivalent to those of the aforementioned (a) to (d), which are advantages of the involute tooth profile.